We demonstrate that in simple 2 x 2 games (cumulative) prospect theory
preferences can be evolutionarily stable, i.e. a population of players with
prospect theory preferences can not be invaded by more rational players. This
holds also if probability weighting is applied to the probabilities of mixed
strategies. We also show that in a typical game with infinitely many strategies,
the “war of attrition”, probability weighting is evolutionarily stable.
Finally, we generalize to other notions of stability. Our results may help to
explain why probability weighting is generally observed in humans, although
it is not optimal in usual decision problems.